Question: Complete the square to solve for $x$. $x^{2}+4x = 0$
Answer: We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. Since the coefficient of our $x$ term is $4$ , half of it would be $2$ , and squaring it gives us ${4}$ $x^2 + 4x { + 4} = 0 { + 4}$ We can now rewrite the left side of the equation as a squared term. $( x + 2 )^2 = 4$ Take the square root of both sides. $x + 2 = \pm2$ Isolate $x$ to find the solution(s). $x = -2\pm2$ So the solutions are: $x = 0 \text{ or } x = -4$ We already found the completed square: $( x + 2 )^2 = 4$